Alg2/Trig E: How can we simplify after we multiply or divide complex numbers?

Alg2/Trig E:  

Let's continue exploring operations of complex numbers by multiplying and dividing. Remember your powers of i--they will come in handy when we want to substitute (especially for "i squared").  

Examples: 
Multiply (3 + i)(4 + 2i)
Multiply (2 + i)(2 - i)  <--What happens to the imaginary unit in the product?

1. Assignment: p.278 / 48, 50, 53, 56, 58, 59, 92

Math 2A: How can we factor the GCF of an expression?

Math 2A:  

What are the factors of two or more monomials? Why should we take the greatest common factor out when we factor an expression? We do this by dividing the expression by the GCF. Does factoring mean we are solving for x? (No.) 

1. Assignment: Worksheet.
   
2. Test corrections (due: 11/5/09).
   

Geometry: How do we write the equations of perpendicular bisectors of line segments?

Geometry:  

What is a perpendicular bisector? How can we use the equation of a perpendicular line and the midpoint of a line segment to write an equation of a perpendicular bisector?

1. Assignment: Worksheet.
2. Test corrections (due: 11/5/09)!
   

Alg2/Trig E: More Practice with Complex Numbers

Alg2/Trig E:  

Sorry I am not in class today! Please work with a partner in the Pair Share Activity. Complete one side of the worksheet and have your partner check your work. You will being receiving the same grade as your partner, so let's work together!

1. Assignment: None.
   

Math 2A: How can we practice multiplying & adding integers?

Math 2A:  

Multiply and add integers without the use of a calculator--this will help you when we start factoring! Let's use these skills to solve diamond puzzles. Can you think of two numbers that have the product of the top number and the sum of the bottom number? 

Example:

1. Assignment: Worksheet a - f.
   
2. Test corrections.

Alg2/Trig E: What is the graphical representation of the sum of complex numbers?

Alg2/Trig E:  

Review the basic powers of i and the cyclic nature of i. Add and subtract complex numbers by "combining like-terms." After you graph two complex numbers, how can you construct a parallelogram? What relationship exists between the two complex numbers and the new vertex?

1. Assignment: p. 277 / 34 - 46 (even)
   

Geometry: What concepts have we mastered in coordinate geometry?

Geometry:  

Let's review how to find the length & midpoint of a line segment. Is the length always positive? Can a line or ray have a midpoint? Also, let's determine whether two lines are parallel or perpendicular (or neither); and write equations of parallel & perpendicular lines. Why do you think vertical & horizontal lines are perpendicular? Why are the lines y = 2 and y = -4 parallel?

1. Test tomorrow!

Alg2/Trig E: What are complex numbers? An imaginary unit?

Alg2/Trig E:  

Introduction to the Complex Number System... How can we represent the "square root of -1"? How do we evaluate different powers of i? What Real Number properties hold in the Complex Number System? What does the graph of a complex number look like?

1. Assignment: Worksheet
   

Geometry: How do we find the length and midpoint of line segments?

Geometry:  

How can we use the ideas from the pair share activity to find the length & midpoint of line segments? How is the Distance Formula related to the Pythagorean Theorem? Why is the midpoint of a segment the average of the x- and y-coordinates? Which method works the best for you?

1. Assignment: Worksheet #16, 18 and p. 38 / 18, 20, 22, 25
   
2. Test on Wednesday!

Math 2A: How can we solve linear equations & inequalities?

Math 2A:  

Let's review for your test! Complete problems about solving linear equations and inequalities. You will have to complete some word problems on the test, so practice translating verbal statements into equations or inequalities

1. Assignment: Finish Review Worksheet
2. Test tomorrow!
   

Alg2/Trig E: Let's review radical expressions & equations!

Alg2/Trig E:  

Sharks vs. Polar Bears! Each team takes turns and tries to obtain a square... When no team gets the square baby seals win!

1. Test tomorrow!
   

Geometry: How do we review parallel & perpendicular lines?

Geometry:  

Let's begin reviewing for our test next week. Take a chance at the spinner and you may land on "Fun & Games!"

1. Assignment: Finish worksheet.
   
2. Test next week!

Math 2A: How can we solve linear inequalities?

Math 2A:  

How can we solve word problems with inequalities? Read the word problems based on The Lord of the Flies (Did you do your reading in English class?); then highlight key phrases and translate the inequalities. Solve the linear inequalities.

1. Assignment: Worksheet
2. Test next Tuesday!
   

Alg2/Trig E: Let's review radical expressions & equations!

Alg2/Trig E:  

Team competition! As a team move around to each station and solve problems about radical expressions, rationalizing the denominator, and radical equations. Record your answers on your team sheet and submit for a chance to win a prize.

1. Test on Friday!
   

Geometry: How do we write the equations of perpendicular lines?

Geometry:  

Investigate the slopes of perpendicular lines. Write the equation of a line perpendicular to an original line through a given point. Use the opposite reciprocal slope and the point to find the appropriate y-intercept. Perpendicular lines do not have the same slopes.

1. Assignment: p. 175 - 176 / 9 - 24 (multiples of 3), 38, 40
2. Test next week!
   

Math 2A: How can we solve linear inequalities?

Math 2A:  

How can we solve linear inequalities like we solve linear equations? These are a bit harder and you may need to combine like-terms or use the Distributive Property before solving. You should still test 0 to determine whether you shade to the left or right.

1. Assignment: Worksheet
2. Test next Tuesday!
   

MathTV.com for Algebra Help!

Please click here: http://www.mathtv.com/

Math 2A: Please go to "Inequalities" --> "Linear, One Variable."
Watch some videos about how to solve linear equations.

Alg2/Trig E: Please go to "Roots and Radicals."
Watch some videos about any of the topics below that category.

Alg2/Trig E: How do we solve radical equations?

Alg2/Trig E:  

How can you solve the radical equation below? What are your initial reactions to this problem? How do you undo a "square root"? How many values of x can there be?

1. Assignment: Worksheet

Math 2A: How can we solve linear inequalities?

Math 2A:  

How can we solve linear inequalities like we solve linear equations? Temporarily change an inequality symbol (ex: >) into an equal sign. Graph your solution on a number line, using an open or closed circle. Then test 0 in the original inequality. This will determine whether you shade to the right or left.

1. Assignment: Worksheet
   

Geometry: How do we write the equations of parallel lines?

Geometry:  

Investigate the slopes of parallel lines. Write the equation of a line parallel to an original line through a given point. Use the same slope and the point to find the appropriate y-intercept. Parallel lines have the same slopes.

1. Assignment: Practice 3.6 B
   

Alg2/Trig E: How do we multiply radical expressions & rationalize denominators?

Alg2/Trig E:  

Let's multiply binomial, radical expressions; what happens to the radical symbol when you multiply like-radicals? How do we rationalize the denominator of a radical expression by multiplying by 1 and using conjugate pairs?

1. Assignment: Worksheet

Math 2A: How can we translate linear inequalities?

Math 2A:  

Let's compare & contrast equations & inequalities... How are they different than expressions? What symbols do we use to represent verbal phrases, such as, "is greater than," "is at most," is no more than," "maximum," etc.

1. Assignment: Worksheet
   

Geometry: What kinds of slopes do parallel & perpendicular lines have?

Geometry:  

Let's review how to find the slope between two points and graphing linear equations in y=mx+b form. Then we will investigate the slopes of parallel & perpendicular lines given special conditions (i.e., parallel to the original line, parallel to the original line through a specific point, etc.).

1. Assignment: p. 168 / 4 - 6, 9, 11 - 14, 18, 24

Alg2/Trig E: How do we simplify, evaluate, & rewrite radical expressions?

Alg2/Trig E:  

How can we rewrite radical expressions with rational exponents? How can we rewrite expressions with rational exponents in radical notation? When can we add, subtract, multiply, & divide radical expressions?

1. Quiz on Friday!
   

Math 2A: How can we solve linear equations?

Math 2A:  

Let's play Math Bingo! Correctly solve for x and win prizes!

1. Assignment: Worksheet (circled problems only).
2. Quiz on Friday!

Geometry: What kind of reasons can we use (and reuse) in proofs?

Geometry:  

Complete proofs about supplementary, complementary, and vertical angles, and line segments. Review for quiz.

1. No homework.
   
2. Quiz on Friday!
   

Math 2A: How can we solve linear equations?

Math 2A:  

Translate a linear equation into English--careful, you will need parentheses today. Use the distributive property and inverse operations to undo what you just said, to solve for the value of a variable. How can we check that the solution is correct? What reasons could you state to justify each step?

1. Assignment: Worksheet.
2. Quiz on Friday!

Alg2/Trig E: What are rational exponents?

Alg2/Trig E:  

How can we rewrite radical expressions with rational exponents? How can we rewrite expressions with rational exponents in radical notation? When can we add & subtract radical expressions?

1. Assignment: Worksheet
   

Geometry: What kind of reasons can we use (and reuse) in proofs?

Geometry:  

When do we use congruence properties in two-column proofs about segments and angles? What are the definitions of supplementary & complementary angles and how can we use these definitions in proofs?

1. Assignment: Practice 2.6 B / 1 - 12.
2. Quiz on Friday!
   

Alg2/Trig E: What is the nth root?

Alg2/Trig E:  

How can we simplify radicals without the use of a calculator and decimals? Which is more accurate? What does "rationalizing the denominator" mean? Do you know your perfect squares and perfect cubes?

02 =	102 =	03 =	103 =
12 =	112 =	13 =	113 =
22 =	122 =	23 =	123 =
32 =	132 =	33 =	133 =
42 =	142 =	43 =	143 =
52 =	152 =	53 =	153 =
62 =	162 =	63 =	163 =
72 =	172 =	73 =	173 =
82 =		83 =
92 =		93 =

1. Assignment: Worksheet
   

Math 2A: How can we solve linear equations?

Math 2A:  

Translate a linear equation into English. Then use inverse operations to undo what you just said, to solve for the value of a variable. How can we check that the solution is correct?

1. Assignment: Worksheet.
2. Quiz on Friday!

Geometry: What does "congruent" mean?

Geometry:  

What is the definition of congruent? How can we use the congruence properties (reflexive, symmetric, & transitive) for proofs about segments and angles?

1. Assignment: p. 105 / 7  and p. 112 – 114 / 2, 3, 12 - 17, 28

Quiz Today!

Geometry: Quiz today!

1. No homework assignment.

Math 2A: Quiz today!

1. No homework assignment.

Alg2/Trig E: Quiz today!

1. No homework assignment.

Quiz on Wednesday!

Geometry:  

What are the equality properties: reflexive, symmetric, & transitive?

1. Assignment: Worksheet
2. Quiz tomorrow! 

Math 2A:  

What is the difference between expressions & equations? Think about what symbols you can use to express the following words or phrases, "is," "3 more than," "the difference," "the quotient."

1. Assignment: Worksheet.
2. Quiz tomorrow!

Alg2/Trig E:  

How can we solve absolute value inequalities and graph the solutions on a number line? How can we analyze the graph to write our solution in symbolic form?

1. Assignment: p. 54 / 49 – 53 and Mixed Review Sheet
   
2. Quiz tomorrow!
   

Geometry: How can we prove solutions to algebraic equations?

Geometry:  

Solving for x and writing reasons for each step is very important in understanding the basics of proofs. Think about the operations you perform and what properties are involved (ex: Distributive Property).

1. Assignment: p. 99 – 100 / 12 – 15, 18, 19, 20, 22
2. Quiz on Wednesday!

Math 2A: How can we use symbols to communicate mathematics?

Math 2A:  

What is the difference between expressions & equations? Think about what symbols you can use to express the following words or phrases, "is," "3 more than," "the difference," "the quotient."

1. Assignment: Worksheet.
2. Quiz on Wednesday!

Alg2/Trig E: How can I use the definition of absolute value to solve equations & inequalities?

Alg2/Trig E:  

Think about the most basic definition of absolute value. Absolute value equations & inequalities will have more than one solution, but always remember that absolute value means, the distance away from zero.

1. Assignment: p. 53 – 54 / 32 – 40 (even), 47, 48, 54, 58
2. Quiz on Wednesday!
   

Test Today!

Geometry: Test today!

1. No homework assignment.

Math 2A: Test today!

1. No homework assignment.

Alg2/Trig E: Test today!

1. No homework assignment.